Scale of the Day: E 7-axis, Construct #1, Lydian Mode - reflected into the first pool

The E 7-axis, Construct #1, Lydian Mode - reflected into the first pool - Scale. The "reflection" being the 1.571 is to 7/4 what 7/4 is to 2.

Scale of the Day: E 7-axis, Construct #1, Lydian Mode - in Square-root-of-2-space

The E 7-axis, Construct #1, Lydian Mode - in Square-root-of-2-space Scale. As the improvising guitarist noted in the comments to yesterday's scale of the day, these 2-note scales exist at the extreme limits of the definition of "scale." While it may be possible to theorize about scales with fewer than 2-notes, there are none that fit my definition.

Definition of a scale: A sequence of intervals that repeats within a larger interval that serves as a harmonic equivalence point, or intervallic basis. In the overwhelming majority of music found the world over this harmonic equivalence point is the octave (2/1).

Today's "scale of the day" poses a couple of challenges. With only 2-notes, it is "harmonically impoverished," resulting in an incredibly restricted intervallic vocabulary. And with the square-root-of-2 (600 cents) serving as the intervallic basis there is the cognitive challenge of treating the "equal-tempered tritone" as a harmonic equivalence - fighting against extensive human conditioning to regard this interval as a particular 'dissonance.' Further complicating this cognitive reality is the fact that a double square-root-of-2 forms the 1200-cent "octave" that is readily heard as harmonically equivalent. The fact that this scale repeats every 600-cents means that it sonically runs the risk of being perceived as a 4-note scale spanning an octave as opposed to the 2-note scale spanning the square-root-of-2 that is conceptually intended.

Scale of the Day: E 7-axis, Construct #1, Lydian Inversion

The E 7-axis, Construct #1, Lydian Inversion Scale. This is one of those "harmonically impoverished" 2-note scales. Here, that second note is the 8/7 major second - an interval I find facinating as an alternative to the more familiar 9/8 major second.